Distribution confusion

Hello

I know that an exponential distribution has the form $\displaystyle f(x) = \lambda e^{-\lambda x}, \: x \geq 0$ but does $\displaystyle f(x) = C_1 e^{-\lambda x} + C_2 e^{-\mu x}, \: x \geq 0$ count as an exponential distribution?
I have tried Google but can only seem to find that a sum of exponential distributions with the same parameter is Erlang distributed, but nothing regarding the above.